void Qov_sq_psi(spinor * const P, spinor * const S) {
Dov_psi(g_spinor_field[DUM_MATRIX], S);
gamma5(g_spinor_field[DUM_MATRIX], g_spinor_field[DUM_MATRIX], VOLUME);
Dov_psi(P,g_spinor_field[DUM_MATRIX]);
gamma5(P,P, VOLUME);
return;
}
void Dov_psi_prec(spinor * const P, spinor * const S) {
/* todo: do preconditioning */
spinorPrecWS *ws=(spinorPrecWS*)g_precWS;
static complex alpha;
Dov_psi(P,S);
alpha.re=-1.;
alpha.im=0.0;
spinorPrecondition(P,P,ws,T,L,alpha,0,1);
}
void ov_check_operator(int t, int x, int y, int z) {
/* Create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], 0, 0);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* Evaluate Dov(psi) */
Dov_psi(g_spinor_field[3], g_spinor_field[2]);
ov_print_spinor(&g_spinor_field[3][g_ipt[t][x][y][z]]);
}
void Qov_sq_psi_prec(spinor * const P, spinor * const S) {
spinorPrecWS *ws=(spinorPrecWS*)g_precWS;
static complex alpha={0,0};
alpha.re=ws->precExpo[0];
spinorPrecondition(P,S,ws,T,L,alpha,0,1);
Dov_psi(g_spinor_field[DUM_MATRIX], P);
gamma5(P, g_spinor_field[DUM_MATRIX], VOLUME);
alpha.re=ws->precExpo[1];
spinorPrecondition(P,P,ws,T,L,alpha,0,1);
Dov_psi(g_spinor_field[DUM_MATRIX], P);
gamma5(P, g_spinor_field[DUM_MATRIX], VOLUME);
alpha.re=ws->precExpo[2];
spinorPrecondition(P,P,ws,T,L,alpha,0,1);
return;
}
void Qov_psi(spinor * const P, spinor * const S) {
Dov_psi(P, S);
gamma5(P, P, VOLUME);
return;
}
/* Checks GW relation only by applying Dov to delta(0,0) */
void ov_check_ginsparg_wilson_relation(void) {
double norm_diff, norm_left, norm_right, norm, max_rel = 0.0, min_left = 1.0e100, min_right = 1.0e100, max_diff = 0.0, min_norm = 1.0e100;
int x, y, z, t, i;
spinor *S_left, *S_right, *S_diff;
/* get memory for the spinor fields */
S_left = ov_alloc_spinor();
S_right = ov_alloc_spinor();
S_diff = ov_alloc_spinor();
/* Create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], 0, 0);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* S_right = D gamma_5 D */
Dov_psi(g_spinor_field[3], g_spinor_field[2]);
gamma5(S_left, g_spinor_field[3], VOLUME);
Dov_psi(S_right, S_left);
/* S_left = {gamma_5, D} */
gamma5(g_spinor_field[3], g_spinor_field[2], VOLUME);
Dov_psi(g_spinor_field[4], g_spinor_field[3]);
add(S_left, S_left, g_spinor_field[4], VOLUME);
/* S_diff = S_left-S_right */
diff(S_diff, S_left, S_right, VOLUME);
/* scan the whole lattice */
printf("// test of the Ginsparg-Wilson relation\n");
for(x=0; x<LX; x++)
for(y = 0; y < LY; y++)
for(z = 0; z < LZ; z++)
for(t = 0; t < T; t++) {
i = g_ipt[t][x][y][z];
_spinor_norm_sq(norm_diff, S_diff[i]);
_spinor_norm_sq(norm_left, S_left[i]);
_spinor_norm_sq(norm_right, S_right[i]);
norm_diff = sqrt(norm_diff);
norm_left = sqrt(norm_left);
norm_right = sqrt(norm_right);
norm = norm_left+norm_right;
if (norm < min_norm)
min_norm = norm;
if (norm > 0.0) {
norm = 2.*norm_diff/norm;
if (norm > max_rel)
max_rel = norm;
}
if (norm_left < min_left)
min_left = norm_left;
if (norm_right < min_right)
min_right = norm_right;
if (norm_diff > max_diff)
max_diff = norm_diff;
}
/* print results */
printf(" - maximum absoulte deviation: %.4le\n", max_diff);
printf(" - maximum relative deviation: %.4le\n", max_rel);
printf(" - minimum mean norm: %4.le\n", min_norm);
printf(" - minimum norm {gamma_5, D}: %.4le\n", min_left);
printf(" - minimum norm D gamma_5 D: %.4le\n", min_right);
/* free memory */
ov_free_spinor(S_left);
ov_free_spinor(S_right);
ov_free_spinor(S_diff);
}
/* Check GW relation with operator norm over the full lattice */
void ov_check_ginsparg_wilson_relation_strong(void) {
double norm_diff, norm_left, norm_right, norm, max_rel = 0.0, min_left = 1.0e100, min_right = 1.0e100, max_diff = 0.0, min_norm = 1.0e100;
int x, y, z, t, i, j, k;
spinor *S_left[4][3], *S_right[4][3], *S_diff[4][3];
if (g_debug_level>0) {
printf("// creating spinor fields and calculating {gamma_5,D} psi and a D gamma_5 D psi\n");
fflush(stdout);
}
for (i=0; i<4; i++)
for (j=0; j<3; j++) {
if (g_debug_level>1) {
printf("// spinor field: delta_dirac at %d, delta_color at %d\n", i, j);
fflush(stdout);
}
/* get memory for the spinor */
S_left[i][j] = ov_alloc_spinor();
S_right[i][j] = ov_alloc_spinor();
S_diff[i][j] = ov_alloc_spinor();
/* Create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], i, j);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* S_right = D gamma_5 D psi */
Dov_psi(g_spinor_field[3], g_spinor_field[2]);
gamma5(S_left[i][j], g_spinor_field[3], VOLUME);
Dov_psi(S_right[i][j], S_left[i][j]);
/* S_left = {gamma_5, D} psi */
gamma5(g_spinor_field[3], g_spinor_field[2], VOLUME);
Dov_psi(g_spinor_field[4], g_spinor_field[3]);
add(S_left[i][j], S_left[i][j], g_spinor_field[4], VOLUME);
/* S_diff = (S_left-S_right) psi, should be zero (GW relation) */
diff(S_diff[i][j], S_left[i][j], S_right[i][j], VOLUME);
}
/* scan the whole lattice and check GW relation */
printf("// test of the Ginsparg-Wilson relation:\n");
if (g_debug_level>0)
fflush(stdout);
for(x=0; x<LX; x++)
for(y = 0; y < LY; y++)
for(z = 0; z < LZ; z++)
for(t = 0; t < T; t++) {
k = g_ipt[t][x][y][z];
norm_diff = ov_operator_colsumnorm(S_diff, k);
norm_left = ov_operator_colsumnorm(S_left, k);
norm_right = ov_operator_colsumnorm(S_right, k);
norm = (norm_left+norm_right)/2.;
if (norm < min_norm)
min_norm = norm;
if (norm > 0.0) {
norm = norm_diff/norm;
if (norm > max_rel)
max_rel = norm;
if ((norm > 1.8) && (g_debug_level)>=5) {
printf("(%d,%d,%d,%d): taxi = %d, rel = %.20le, lr = [%.4le, %.4le], diff = %.4le\n", t, x, y, z, ((x>LX/2) ? LX-x : x)+((y>LY/2) ? LY-y : y)+((z>LZ/2) ? LZ-z : z)+((t>T/2) ? T-t : t), norm, norm_left, norm_right, norm_diff);
printf("// left[0][0]:\n");
ov_print_spinor(&S_left[0][0][k]);
printf("// right[0][0]:\n");
ov_print_spinor(&S_right[0][0][k]);
printf("// diff[0][0]:\n");
ov_print_spinor(&S_diff[0][0][k]);
}
}
if (norm_left < min_left)
min_left = norm_left;
if (norm_right < min_right)
min_right = norm_right;
if (norm_diff > max_diff)
max_diff = norm_diff;
}
/* print results */
printf(" - maximum absolute deviation: %.4le\n", max_diff);
printf(" - maximum relative deviation: %.4le\n", max_rel);
printf(" - minimum mean norm: %.4le\n", min_norm);
printf(" - minimum norm {gamma_5, D}: %.4le\n", min_left);
printf(" - minimum norm D gamma_5 D: %.4le\n", min_right);
/* free memory */
for (i=0; i<4; i++)
for (j=0; j<3; j++) {
ov_free_spinor(S_left[i][j]);
ov_free_spinor(S_right[i][j]);
ov_free_spinor(S_diff[i][j]);
}
}
/* saves the operator to the given filename */
void ov_save_12x12(const char * pFileName) {
int i, j, k, x, y, z, t;
spinor *s[4][3];
matrix12x12 mat;
FILE * pCompare;
/* evaluate Dov(psi) */
for (i=0; i<4; i++)
for (j=0; j<3; j++) {
/* get memory for the spinor */
s[i][j] = ov_alloc_spinor();
/* create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], i, j);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* apply Dov */
Dov_psi(s[i][j], g_spinor_field[2]);
}
/* open file for storing the operator */
pCompare = fopen(pFileName, "w");
if (pCompare == NULL) {
fprintf(stderr, "Error: could not open '%s' for writing the operator\n", pFileName);
exit(1);
}
for(t = 0; t < T; t++){
for(x = 0; x < LX; x++){
for(y = 0; y < LY; y++){
for(z=0; z<LZ; z++) {
k = g_ipt[t][x][y][z];
for (j=0; j<3; j++)
for (i=0; i<4; i++) {
mat[0][i+4*j] = s[i][j][k].s0.c0;
mat[1][i+4*j] = s[i][j][k].s1.c0;
mat[2][i+4*j] = s[i][j][k].s2.c0;
mat[3][i+4*j] = s[i][j][k].s3.c0;
mat[4][i+4*j] = s[i][j][k].s0.c1;
mat[5][i+4*j] = s[i][j][k].s0.c1;
mat[6][i+4*j] = s[i][j][k].s1.c1;
mat[7][i+4*j] = s[i][j][k].s2.c1;
mat[8][i+4*j] = s[i][j][k].s3.c2;
mat[9][i+4*j] = s[i][j][k].s1.c2;
mat[10][i+4*j] = s[i][j][k].s2.c2;
mat[11][i+4*j] = s[i][j][k].s3.c2;
}
for (i=0;i<12; i++)
for (j=0; j<12; j++)
fprintf(pCompare, "%.20le %.20le ", creal(mat[i][j]), cimag(mat[i][j]));
}
}
}
}
/* close file */
fclose(pCompare);
/* free memory */
for (i=0; i<4; i++)
for (j=0; j<3; j++)
ov_free_spinor(s[i][j]);
}
/* compares the operator with the one given in pFileName */
void ov_compare_12x12(const char * pFileName) {
double norm, rel, *max_rel, *max_abs, Max_rel = 0.0, Max_abs = 0.0;
int i, j, k, x, x_taxi, y, y_taxi, z, z_taxi, t, t_taxi, maxtaxi, taxi;
spinor *s[4][3];
matrix12x12 mat, mat2, diff;
FILE * pCompare;
/* evaluate Dov(psi) */
for (i=0; i<4; i++)
for (j=0; j<3; j++) {
/* get memory for the spinor */
s[i][j] = ov_alloc_spinor();
/* create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], i, j);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* apply Dov */
Dov_psi(s[i][j], g_spinor_field[2]);
}
/* init locality table */
maxtaxi = (LX/2)+(LY/2)+(LZ/2)+T/2;
max_abs = (double*)calloc(maxtaxi+1, sizeof(double));
max_rel = (double*)calloc(maxtaxi+1, sizeof(double));
for(i = 0; i <= maxtaxi; i++) {
max_abs[i] = 0.0;
max_rel[i] = 0.0;
}
/* open file containing operator for comparison */
pCompare = fopen(pFileName, "r");
if (pCompare == NULL) {
fprintf(stderr, "Error: could not open '%s' for comparison of operator\n", pFileName);
exit(1);
}
/* fill locality table */
if (g_debug_level > 0) {
printf("// beginning comparison\n");
fflush(stdout);
}
for(t = 0; t < T; t++){
t_taxi = (t > T/2) ? T - t : t;
for(x = 0; x < LX; x++){
x_taxi = (x > LX/2) ? LX-x : x;
for(y = 0; y < LY; y++){
y_taxi = (y > LY/2) ? LY-y : y;
for(z=0; z<LZ; z++) {
z_taxi = (z > LZ/2) ? LZ-z : z;
taxi = x_taxi + y_taxi + z_taxi + t_taxi;
k = g_ipt[t][x][y][z];
for (j=0; j<3; j++)
for (i=0; i<4; i++) {
mat[0][i+4*j] = s[i][j][k].s0.c0;
mat[1][i+4*j] = s[i][j][k].s1.c0;
mat[2][i+4*j] = s[i][j][k].s2.c0;
mat[3][i+4*j] = s[i][j][k].s3.c0;
mat[4][i+4*j] = s[i][j][k].s0.c1;
mat[5][i+4*j] = s[i][j][k].s0.c1;
mat[6][i+4*j] = s[i][j][k].s1.c1;
mat[7][i+4*j] = s[i][j][k].s2.c1;
mat[8][i+4*j] = s[i][j][k].s3.c2;
mat[9][i+4*j] = s[i][j][k].s1.c2;
mat[10][i+4*j] = s[i][j][k].s2.c2;
mat[11][i+4*j] = s[i][j][k].s3.c2;
}
for (i=0;i<12; i++)
for (j=0; j<12; j++)
fscanf(pCompare, "%le %le", (double*)&mat2[i][j], (double*)&mat2[i][j] + 1);
ov_matrix12x12_diff(diff, mat, mat2);
/* statistics */
norm = ov_matrix12x12_rowsumnorm(diff);
if (norm > max_abs[taxi]) {
max_abs[taxi] = norm;
if (norm > Max_abs)
Max_abs = norm;
}
rel = (ov_matrix12x12_rowsumnorm(mat) + ov_matrix12x12_rowsumnorm(mat2))/2;
if (rel>0.0) {
rel = norm/rel;
if (rel > max_rel[taxi]) {
max_rel[taxi] = rel;
if (rel > Max_rel)
Max_rel = rel;
}
}
}
}
}
}
/* print locality table */
printf("// comparison of overlap operator to %s\n", pFileName);
printf(" - maximum absolute deviation: %.4le\n", Max_abs);
printf(" - maximum relative deviation: %.4le\n", Max_rel);
printf("// taxi | max abs | max rel\n");
for(i = 0; i <= maxtaxi; i++)
printf("%7d %10.6le %10.6le\n", i, max_abs[i], max_rel[i]);
printf("\n");
/* close file */
fclose(pCompare);
/* free memory */
free(max_abs);
free(max_rel);
for (i=0; i<4; i++)
for (j=0; j<3; j++)
ov_free_spinor(s[i][j]);
}
void ov_check_locality() {
double norm, *maxnorm, *minnorm, *avgnorm;
int i, j, k, x, x_taxi, y, y_taxi, z, z_taxi, t, t_taxi, maxtaxi, *samples, taxi;
spinor *s[4][3];
/* evaluate Dov(psi) */
for (i=0; i<4; i++)
for (j=0; j<3; j++) {
/* get memory for the spinor */
s[i][j] = ov_alloc_spinor();
/* create delta source at origin */
source_spinor_field(g_spinor_field[1], g_spinor_field[0], i, j);
convert_eo_to_lexic(g_spinor_field[2], g_spinor_field[1], g_spinor_field[0]);
/* apply Dov */
Dov_psi(s[i][j], g_spinor_field[2]);
}
/* init locality table */
maxtaxi = (LX/2)+(LY/2)+(LZ/2)+T/2;
maxnorm = (double*)calloc(maxtaxi+1, sizeof(double));
minnorm = (double*)calloc(maxtaxi+1, sizeof(double));
avgnorm = (double*)calloc(maxtaxi+1, sizeof(double));
samples = (int*)calloc(maxtaxi+1, sizeof(int));
for(i = 0; i <= maxtaxi; i++) {
maxnorm[i] = 0.;
minnorm[i] = 1.0e100;
avgnorm[i] = 0.;
samples[i] = 0;
}
/* fill locality table */
printf("// beginning locality test\n");
for(x=0; x<LX; x++) {
x_taxi = (x > LX/2) ? LX-x : x;
for(y = 0; y < LY; y++){
y_taxi = (y > LY/2) ? LY-y : y;
for(z = 0; z < LZ; z++){
z_taxi = (z > LZ/2) ? LZ-z : z;
for(t = 0; t < T; t++){
t_taxi = (t > T/2) ? T - t : t;
taxi = x_taxi + y_taxi + z_taxi + t_taxi;
k = g_ipt[t][x][y][z];
norm = ov_operator_colsumnorm(s, k);
// statistics
if (norm > maxnorm[taxi])
maxnorm[taxi] = norm;
if (norm < minnorm[taxi])
minnorm[taxi] = norm;
avgnorm[taxi] += norm;
samples[taxi]++;
}
}
}
}
/* print locality table */
printf("// locality check of overlap operator\n");
printf("// taxi | max norm | avg norm | min norm | #samples\n");
for(i = 0; i <= maxtaxi; i++)
printf("%7d %10.6le %10.6le %10.6le %8d\n", i, maxnorm[i], (double)(avgnorm[i]/samples[i]), minnorm[i], samples[i]);
printf("\n");
/* free memory */
free(maxnorm);
free(minnorm);
free(avgnorm);
free(samples);
for (i=0; i<4; i++)
for (j=0; j<3; j++)
ov_free_spinor(s[i][j]);
}